Question

write a balanced equation for the following by inserting the necessary and correct coefficients.

\\(\text{sio}_2(s) + \text{c}(s) + \text{mg}_3(\text{po}_4)_2(s) \
ightarrow \text{co}(g) + \text{p}_4(s) + \text{mgsio}_3(s)\\)

Explanation:

Identify elements to balance

We need to balance the chemical equation:

$$ a\,\text{SiO}_2(s) + b\,\text{C}(s) + c\,\text{Mg}_3(\text{PO}_4)_2(s) ightarrow d\,\text{CO}(g) + e\,\text{P}_4(s) + f\,\text{MgSiO}_3(s) $$

We list the elements involved: \(\text{Si}\), \(\text{O}\), \(\text{C}\), \(\text{Mg}\), and \(\text{P}\).

Set up element balance equations

We write equations for each element based on coefficients:

• Magnesium (\(\text{Mg}\)): \(3c = f\)
• Phosphorus (\(\text{P}\)): \(2c = 4e\)
• Silicon (\(\text{Si}\)): \(a = f\)
• Oxygen (\(\text{O}\)): \(2a + 8c = d + 3f\)
• Carbon (\(\text{C}\)): \(b = d\)

Solve the system of equations

Let us choose a convenient value for one coefficient to find integer solutions:

• Set \(e = 1\).
• From \(\text{P}\) balance: \(2c = 4(1) \implies c = 2\).
• From \(\text{Mg}\) balance: \(f = 3c = 3(2) = 6\).
• From \(\text{Si}\) balance: \(a = f = 6\).
• From \(\text{O}\) balance:

$$ 2(6) + 8(2) = d + 3(6) $$

$$ 12 + 16 = d + 18 $$

$$ 28 = d + 18 \implies d = 10 $$

• From \(\text{C}\) balance: \(b = d = 10\).

Verify the balanced coefficients

Let's check the atom counts with \(a=6\), \(b=10\), \(c=2\), \(d=10\), \(e=1\), \(f=6\):

• \(\text{Si}\): Left \(6\), Right \(6\) (Balanced)
• \(\text{C}\): Left \(10\), Right \(10\) (Balanced)
• \(\text{Mg}\): Left \(2 \times 3 = 6\), Right \(6\) (Balanced)
• \(\text{P}\): Left \(2 \times 2 = 4\), Right \(4\) (Balanced)
• \(\text{O}\): Left \(6 \times 2 + 2 \times 8 = 12 + 16 = 28\), Right \(10 \times 1 + 6 \times 3 = 10 + 18 = 28\) (Balanced)

Answer:

Write a balanced equation for the following by inserting the necessary and correct coefficients.

<blank>\(6\text{SiO}_2(s) + 10\text{C}(s) + 2\text{Mg}_3(\text{PO}_4)_2(s)
ightarrow 10\text{CO}(g) + \text{P}_4(s) + 6\text{MgSiO}_3(s)\)</blank>